Question

evaluate the expression.
$(7.5 \times 10^4) \div (3 \times 10^1)$
$? \times 10$

Explanation:

Step1: Split the coefficients and powers

Separate the terms into coefficient and power parts:
$$\frac{7.5}{3} \times \frac{10^4}{10^1}$$

Step2: Calculate coefficient division

Divide the numerical coefficients:
$$\frac{7.5}{3} = 2.5$$

Step3: Simplify power of 10

Use exponent rule $\frac{10^a}{10^b}=10^{a-b}$:
$$\frac{10^4}{10^1} = 10^{4-1} = 10^3$$

Step4: Combine the results

Multiply the two simplified terms together:
$$2.5 \times 10^3$$

Answer:

$2.5 \times 10^3$